以下代码是初期写的代码，后来对代码进行优化，解决了初期的bug。完整的选择城市三级联动组件可以参考我的github项目中的代码，这是后期调试成功上传上去的React选择城市三级联动组件

<SelectArea allAreaInfo={allAreaInfo} province={province} city={city} district={district} cancel={this.closeModal} confirm={this.SelectAddress} />

import React,{ Component,PropTypes } from 'react';
import { connect } from 'react-redux';
import { Link } from 'react-router';
import rest from '../../lib/rest';

const HEIGHT = 36;
export class Picker extends Component {
  constructor(props) {
    super(props);
    this.state = {
      selectedIndex: this.props.index
    };
    this.onScroll = this.onScroll.bind(this);
    this.resetPosition = this.resetPosition.bind(this);
  }

  componentDidMount() {
    this.refs.scroller.scrollTop = this.state.selectedIndex * HEIGHT;
    this.refs.scroller.addEventListener('touchstart',this.touchStart,false);
    this.refs.scroller.addEventListener('touchend',this.touchEnd,false);
    this.refs.scroller.addEventListener('mousedown',false);
    this.refs.scroller.addEventListener('mouseup',false);
  }

  touchStart() {
    this.isTouchStart = true;
  }

  touchEnd() {
    this.isTouchStart = false;
    if (this.timer) clearTimeout(this.timer);
    this.timer = setTimeout(this.resetPosition,100);
  }

  onScroll() {
    if (this.timer) clearTimeout(this.timer);
    this.timer = setTimeout(this.resetPosition,100);
  }

  resetPosition() {
    let provinceList = [],cityList = [],districtList = [];
    const { type = '',allAreaInfo = [],callback = () => { } } = this.props;
    if (this.isTouchStart) return;
    const top = this.refs.scroller.scrollTop;
    const distance = top % HEIGHT;
    let target;
    if (distance > HEIGHT / 2) {
      target = top + HEIGHT - distance;
      this.refs.scroller.scrollTop = target;
    } else {
      target = top - distance;
      this.refs.scroller.scrollTop = target;
    }
    const selectedIndex = target / HEIGHT;
    this.setState({
      selectedIndex
    },() => {
      callback(type,selectedIndex);
    });
  }

  render() {
    const { list = [] } = this.props;
    return (
      <div className="ul-area" onScroll={this.onScroll} ref="scroller">
        <ul>
          <li></li>
          {
            list.map((item,index) => (
              <li key={index} className={`${index === this.state.selectedIndex && 'selected'}`}>{item}</li>
            ))
          }
          <li></li>
        </ul>
      </div>
    )
  }
}

class SelectArea extends Component {
  constructor(props) {
    super(props);
    this.state = {
      provinceList: [],cityList: [],districtList: [],provinceIndex: 0,cityIndex: 0,districtIndex: 0,showPicker: false
    };
    this.handleSelect = this.handleSelect.bind(this);
  }

  componentDidMount() {
    const { allAreaInfo = [],province = '',city = '',district = '' } = this.props;
    let provinceList = [],districtList = [],provinceIndex = 0,cityIndex = 0,districtIndex = 0;
    if (province) {
      provinceIndex = allAreaInfo.findIndex(item => item.name === province);
      cityIndex = allAreaInfo[provinceIndex].city.findIndex(item => item.name === city);
      districtIndex = allAreaInfo[provinceIndex].city[cityIndex].area.findIndex(item => item === (district || '其他'));
      this.setState({
        provinceIndex,cityIndex,districtIndex,showPicker: true
      });
    }
    allAreaInfo.forEach(item => provinceList.push(item.name));
    if (allAreaInfo[provinceIndex].city.length) {
      allAreaInfo[provinceIndex].city.forEach(item => cityList.push(item.name));
    }
    this.setState({
      provinceList,cityList,districtList: allAreaInfo[provinceIndex].city[cityIndex] && allAreaInfo[provinceIndex].city[cityIndex].area,showPicker: true
    });
  }

  handleSelect(type,index) {
    let provinceList = [],districtList = [];
    const { provinceIndex,districtIndex } = this.state;
    const { allAreaInfo = [] } = this.props;
    switch(type) {
      case 'province':
        allAreaInfo[index].city.forEach(item => cityList.push(item.name));
        this.setState({
          provinceIndex: index,districtList: allAreaInfo[index].city[0] && allAreaInfo[index].city[0].area
        });
        break;
      case 'city':
        this.setState({
          cityIndex: index,districtList: allAreaInfo[provinceIndex].city[index] && allAreaInfo[provinceIndex].city[index].area
        });
        break;
      case 'district':
        this.setState({
          districtIndex: index,districtList: allAreaInfo[provinceIndex].city[cityIndex].area
        });
        break;
      default:
        break;
    }
  }

  render() {
    const { allAreaInfo = [],cancel = () => {},confirm = () => {} } = this.props;
    const { provinceList,districtList,provinceIndex,districtIndex } = this.state;
    return (
      <div id="select-area">
        <div className="col-xs-12 select-area" onClick={e => e.stopPropagation()}>
          <div className="row border-bottom-grey">
            <div className="col-xs-6" onClick={cancel}>取消</div>
            <div className="col-xs-6 text-right font-orange"
            onClick={confirm.bind(null,districtIndex)}>确定</div>
          </div>
          {
            this.state.showPicker && (
              <div className="row list">
                <Picker type="province" allAreaInfo={allAreaInfo} list={provinceList} 
                index={this.state.provinceIndex} callback={this.handleSelect} />
                <Picker type="city" allAreaInfo={allAreaInfo} list={cityList} 
                index={cityIndex} callback={this.handleSelect} />
                <Picker type="district" allAreaInfo={allAreaInfo} list={districtList} 
                index={districtIndex} callback={this.handleSelect} />
              </div>
            )
          }
        </div>
      </div>
    )
  }
}

SelectArea.contextTypes = {
  router: PropTypes.object.isrequired
};
SelectArea.propTypes = {
  // test: PropTypes.string.isrequired,
};
export default connect(state => (state))(SelectArea);